RESEARCH AREA. Basic neuroscience involving structure/function relations for neuronal dendritic branching, dendritic spines, and synapses (also neuron populations, with cortical symmetry), and for such functions as synaptic transmission, amplification and dendro-dendritic interactions in the context of spatio-temporal input patterns, logical processing of input, and neural plasticity, as in conditioning and learning. RATIONALE. Combine experimental data from neuroanatomy and from electrophysiology with biophysical models of nerve membrane (passive, synaptic and excitable) into a comprehensive theory which can lead to new insights and to testable theoretical predictions (leading to the design of better experiments). To do this, we must create, explore and test mathematical and computational models with different degrees of complexity. METHODOLOGY. Our methods include both analytical solutions and computational solutions of boundary value problems (for partial differential equations) in the traditions of classical physics. They include also the formulation and solutions of problems in terms of systems of ordinary differential equations; when this is done explicitly for a compartmental model of a neuron, it is possible to accommodate a remarkable variety of dendritic branching patterns and non-uniform distributions of membrane properties and of synaptic inputs. RESULTS. Perspective, results and references can be found in a recent review and in chapters in several recent books: see the Oct 1992 special issue of Physiological Reviews, 72:S159-S186; see also "Single Neuron Computation: (T. McKenna, J. Davis and S. F. Zornetzer, eds) Academic Press, 1992, and "Computational Neuroscience" (E. L. Schwartz, ed.) MIT Press, 1990.